See also

R = SerialLink(links, options) is a robot object defined by a vector
of Link class objects which can be instances of Link, Revolute,
Prismatic, RevoluteMDH or PrismaticMDH.

R = SerialLink(options) is a null robot object with no links.

R = SerialLink([R1 R2 ...], options) concatenate robots, the base of
R2 is attached to the tip of R1. Can also be written R1*R2 etc.

R = SerialLink(R1, options) is a deep copy of the robot object R1,
with all the same properties.

R = SerialLink(dh, options) is a robot object with kinematics defined
by the matrix dh which has one row per joint and each row is
[theta d a alpha] and joints are assumed revolute. An optional
fifth column sigma indicate revolute (sigma=0, default) or
prismatic (sigma=1).

Notes

qdd = R.accel(q, qd, torque) is a vector (Nx1) of joint accelerations that result
from applying the actuator force/torque to the manipulator robot R in
state q and qd, and N is the number of robot joints.

If q, qd, torque are matrices (KxN) then qdd is a matrix (KxN) where each row
is the acceleration corresponding to the equivalent rows of q, qd, torque.

qdd = R.accel(x) as above but x=[q,qd,torque] (1x3N).

Note

Useful for simulation of manipulator dynamics, in
conjunction with a numerical integration function.

Uses the method 1 of Walker and Orin to compute the forward dynamics.

Featherstone's method is more efficient for robots with large numbers
of joints.

m = R.cinertia(q) is the NxN Cartesian (operational space) inertia matrix which relates
Cartesian force/torque to Cartesian acceleration at the joint configuration q, and N
is the number of robot joints.

See also

C = R.collisions(q, model) is true if the SerialLink object R at
pose q (1xN) intersects the solid model model which belongs to the
class CollisionModel. The model comprises a number of geometric
primitives and associate pose.

C = R.collisions(q, model, dynmodel, tdyn) as above but also checks
dynamic collision model dynmodel whose elements are at pose tdyn.
tdyn is an array of transformation matrices (4x4xP), where
P = length(dynmodel.primitives). The P'th plane of tdyn premultiplies the
pose of the P'th primitive of dynmodel.

Author

See also

C = R.coriolis(q, qd) is the Coriolis/centripetal matrix (NxN) for
the robot in configuration q and velocity qd, where N is the number of
joints. The product C*qd is the vector of joint force/torque due to velocity
coupling. The diagonal elements are due to centripetal effects and the
off-diagonal elements are due to Coriolis effects. This matrix is also
known as the velocity coupling matrix, since it describes the disturbance forces
on any joint due to velocity of all other joints.

If q and qd are matrices (KxN), each row is interpretted as a joint state
vector, and the result (NxNxK) is a 3d-matrix where each plane corresponds
to a row of q and qd.

C = R.coriolis( qqd) as above but the matrix qqd (1x2N) is [qqd].

Notes

Joint viscous friction is also a joint force proportional to velocity but it is
eliminated in the computation of this value.

[T,q,qd] = R.fdyn(T, torqfun) integrates the dynamics of the robot over
the time interval 0 to T and returns vectors of time T, joint position q
and joint velocity qd. The initial joint position and velocity are zero.
The torque applied to the joints is computed by the user-supplied control
function torqfun:

TAU = TORQFUN(T, Q, QD)

where q and qd are the manipulator joint coordinate and velocity state
respectively, and T is the current time.

[ti,q,qd] = R.fdyn(T, torqfun, q0, qd0) as above but allows the initial
joint position and velocity to be specified.

See also

T = R.fkine(q, options) is the pose of the robot end-effector as an SE(3)
homogeneous transformation (4x4) for the joint configuration q (1xN).

If q is a matrix (KxN) the rows are interpreted as the generalized joint
coordinates for a sequence of points along a trajectory. q(i,j) is the
j'th joint parameter for the i'th trajectory point. In this case T is a
3d matrix (4x4xK) where the last subscript is the index along the path.

[T,all] = R.fkine(q) as above but all (4x4xN) is the pose of the link
frames 1 to N, such that all(:,:,k) is the pose of link frame k.

Options

'deg'

Assume that revolute joint coordinates are in degrees not
radians

Note

The robot's base or tool transform, if present, are incorporated into the
result.

Joint offsets, if defined, are added to Q before the forward kinematics are
computed.

See also

[tau,jac0] = R.gravjac(q) is the generalised joint force/torques due to
gravity (1xN) and the manipulator Jacobian in the base frame (6xN) for
robot pose q (1xN), where N is the number of robot joints.

[tau,jac0] = R.gravjac(q,grav) as above but gravity is given explicitly
by grav (3x1).

Trajectory operation

If q is MxN where N is the number of robot joints then a trajectory is
assumed where each row of q corresponds to a pose. tau (MxN) is the
generalised joint torque, each row corresponding to an input pose, and
jac0 (6xNxM) where each plane is a Jacobian corresponding to an input pose.

Notes

The gravity vector is defined by the SerialLink property if not explicitly given.

Does not use inverse dynamics function RNE.

Faster than computing gravity and Jacobian separately.

Author

Bryan Moutrie

See also

taug = R.gravload(q) is the joint gravity loading (1xN) for the robot R
in the joint configuration q (1xN), where N is the number of robot
joints. Gravitational acceleration is a property of the robot object.

If q is a matrix (MxN) each row is interpreted as a joint configuration
vector, and the result is a matrix (MxN) each row being the corresponding
joint torques.

taug = R.gravload(q, grav) as above but the gravitational
acceleration vector grav is given explicitly.

See also

q = R.ikcon(T) are the joint coordinates (1xN) corresponding to the robot
end-effector pose T (4x4) which is a homogenenous transform.

[q,err] = robot.ikcon(T) as above but also returns err which is the
scalar final value of the objective function.

[q,err,exitflag] = robot.ikcon(T) as above but also returns the
status exitflag from fmincon.

[q,err,exitflag] = robot.ikcon(T, q0) as above but specify the
initial joint coordinates q0 used for the minimisation.

[q,err,exitflag] = robot.ikcon(T, q0, options) as above but specify the
options for fmincon to use.

Trajectory operation

In all cases if T is 4x4xM it is taken as a homogeneous transform
sequence and R.ikcon() returns the joint coordinates corresponding to
each of the transforms in the sequence. q is MxN where N is the number
of robot joints. The initial estimate of q for each time step is taken as
the solution from the previous time step.

err and exitflag are also Mx1 and indicate the results of optimisation
for the corresponding trajectory step.

Notes

Requires fmincon from the Optimization Toolbox.

Joint limits are considered in this solution.

Can be used for robots with arbitrary degrees of freedom.

In the case of multiple feasible solutions, the solution returned
depends on the initial choice of Q0.

Works by minimizing the error between the forward kinematics of the
joint angle solution and the end-effector frame as an optimisation.
The objective function (error) is described as:

Underactuated robots

For the case where the manipulator has fewer than 6 DOF the solution
space has more dimensions than can be spanned by the manipulator joint
coordinates.

q = R.ikine(T, q0, m, options) similar to above but where m is a mask
vector (1x6) which specifies the Cartesian DOF (in the wrist coordinate
frame) that will be ignored in reaching a solution. The mask vector
has six elements that correspond to translation in X, Y and Z, and rotation
about X, Y and Z respectively. The value should be 0 (for ignore) or 1.
The number of non-zero elements should equal the number of manipulator DOF.

For robots with 4 or 5 DOF this method is very difficult to use since
orientation is specified by T in world coordinates and the achievable
orientations are a function of the tool position.

Trajectory operation

In all cases if T is 4x4xM it is taken as a homogeneous transform sequence
and R.ikine() returns the joint coordinates corresponding to each of the
transforms in the sequence. q is MxN where N is the number of robot joints.
The initial estimate of q for each time step is taken as the solution
from the previous time step.

Options

'pinv'

use pseudo-inverse instead of Jacobian transpose (default)

'ilimit', L

set the maximum iteration count (default 1000)

'tol', T

set the tolerance on error norm (default 1e-6)

'alpha', A

set step size gain (default 1)

'varstep'

enable variable step size if pinv is false

'verbose'

show number of iterations for each point

'verbose=2'

show state at each iteration

'plot'

plot iteration state versus time

References

Robotics, Vision & Control, Section 8.4,
P. Corke, Springer 2011.

Notes

Solution is computed iteratively.

Solution is sensitive to choice of initial gain. The variable
step size logic (enabled by default) does its best to find a balance
between speed of convergence and divergence.

Some experimentation might be required to find the right values of
tol, ilimit and alpha.

The pinv option leads to much faster convergence (default)

The tolerance is computed on the norm of the error between current
and desired tool pose. This norm is computed from distances
and angles without any kind of weighting.

The inverse kinematic solution is generally not unique, and
depends on the initial guess Q0 (defaults to 0).

The default value of Q0 is zero which is a poor choice for most
manipulators (eg. puma560, twolink) since it corresponds to a kinematic
singularity.

Such a solution is completely general, though much less efficient
than specific inverse kinematic solutions derived symbolically, like
ikine6s or ikine3.

This approach allows a solution to be obtained at a singularity, but
the joint angles within the null space are arbitrarily assigned.

Joint offsets, if defined, are added to the inverse kinematics to
generate Q.

Joint limits are not considered in this solution.

See also

q = R.ikine3(T) is the joint coordinates corresponding to the robot
end-effector pose T represented by the homogenenous transform. This
is a analytic solution for a 3-axis robot (such as the first three joints
of a robot like the Puma 560).

q = R.ikine3(T, config) as above but specifies the configuration of the arm in
the form of a string containing one or more of the configuration codes:

'l'

arm to the left (default)

'r'

arm to the right

'u'

elbow up (default)

'd'

elbow down

Notes

The same as IKINE6S without the wrist.

The inverse kinematic solution is generally not unique, and
depends on the configuration string.

Joint offsets, if defined, are added to the inverse kinematics to
generate Q.

Reference

Inverse kinematics for a PUMA 560 based on the equations by Paul and Zhang
From The International Journal of Robotics Research
Vol. 5, No. 2, Summer 1986, p. 32-44

Author

See also

q = R.ikine6s(T) is the joint coordinates (1xN) corresponding to the robot
end-effector pose T represented by an SE(3) homogenenous transform (4x4). This
is a analytic solution for a 6-axis robot with a spherical wrist (the most
common form for industrial robot arms).

If T represents a trajectory (4x4xM) then the inverse kinematics is
computed for all M poses resulting in q (MxN) with each row representing
the joint angles at the corresponding pose.

q = R.IKINE6S(T, config) as above but specifies the configuration of the arm in
the form of a string containing one or more of the configuration codes:

'l'

arm to the left (default)

'r'

arm to the right

'u'

elbow up (default)

'd'

elbow down

'n'

wrist not flipped (default)

'f'

wrist flipped (rotated by 180 deg)

Notes

Treats a number of specific cases:

Robot with no shoulder offset

Robot with a shoulder offset (has lefty/righty configuration)

Robot with a shoulder offset and a prismatic third joint (like Stanford arm)

See also

q = R.IKINE_SYM(k, options) is a cell array (Cx1) of inverse kinematic
solutions of the SerialLink object ROBOT. The cells of q represent the
different possible configurations. Each cell of q is a vector (Nx1), and
element J is the symbolic expressions for the J'th joint angle. The
solution is in terms of the desired end-point pose of the robot which is
represented by the symbolic matrix (3x4) with elements

nx ox ax tx
ny oy ay ty
nz oz az tz

where the first three columns specify orientation and the last column
specifies translation.

In all cases if T is 4x4xM it is taken as a homogeneous transform sequence
and R.ikinem() returns the joint coordinates corresponding to each of the
transforms in the sequence. q is MxN where N is the number of robot joints.
The initial estimate of q for each time step is taken as the solution
from the previous time step.

Options

Stiffness used to impose a smoothness contraint on joint
angles, useful when N is large (default 0)

'qlimits'

Enforce joint limits

'ilimit', L

Iteration limit (default 1000)

'nolm'

Disable Levenberg-Marquadt

Notes

PROTOTYPE CODE UNDER DEVELOPMENT, intended to do numerical inverse kinematics
with joint limits

The inverse kinematic solution is generally not unique, and
depends on the initial guess Q0 (defaults to 0).

The function to be minimized is highly nonlinear and the solution is
often trapped in a local minimum, adjust Q0 if this happens.

The default value of Q0 is zero which is a poor choice for most
manipulators (eg. puma560, twolink) since it corresponds to a kinematic
singularity.

Such a solution is completely general, though much less efficient
than specific inverse kinematic solutions derived symbolically, like
ikine6s or ikine3.% - Uses Levenberg-Marquadt minimizer LMFsolve if it can be found,
if 'nolm' is not given, and 'qlimits' false

The error function to be minimized is computed on the norm of the error
between current and desired tool pose. This norm is computed from distances
and angles and 'pweight' can be used to scale the position error norm to
be congruent with rotation error norm.

This approach allows a solution to obtained at a singularity, but
the joint angles within the null space are arbitrarily assigned.

Joint offsets, if defined, are added to the inverse kinematics to
generate Q.

See also

q = R.ikunc(T) are the joint coordinates (1xN) corresponding to the robot
end-effector pose T (4x4) which is a homogenenous transform, and N is the
number of robot joints.

[q,err] = robot.ikunc(T) as above but also returns err which is the
scalar final value of the objective function.

[q,err,exitflag] = robot.ikunc(T) as above but also returns the
status exitflag from fminunc.

[q,err,exitflag] = robot.ikunc(T, q0) as above but specify the
initial joint coordinates q0 used for the minimisation.

[q,err,exitflag] = robot.ikunc(T, q0, options) as above but specify the
options for fminunc to use.

Trajectory operation

In all cases if T is 4x4xM it is taken as a homogeneous transform
sequence and R.ikunc() returns the joint coordinates corresponding to
each of the transforms in the sequence. q is MxN where N is the number
of robot joints. The initial estimate of q for each time step is taken as
the solution from the previous time step.

err and exitflag are also Mx1 and indicate the results of optimisation
for the corresponding trajectory step.

Notes

Requires fminunc from the Optimization Toolbox.

Joint limits are not considered in this solution.

Can be used for robots with arbitrary degrees of freedom.

In the case of multiple feasible solutions, the solution returned
depends on the initial choice of Q0

Works by minimizing the error between the forward kinematics of the
joint angle solution and the end-effector frame as an optimisation.
The objective function (error) is described as:

Note

See also

j0 = R.jacob0(q, options) is the Jacobian matrix (6xN) for the robot in
pose q (1xN), and N is the number of robot joints. The manipulator
Jacobian matrix maps joint velocity to end-effector spatial velocity V =
j0*QD expressed in the world-coordinate frame.

References

See also

jn = R.jacobn(q, options) is the Jacobian matrix (6xN) for the robot in
pose q, and N is the number of robot joints. The manipulator Jacobian
matrix maps joint velocity to end-effector spatial velocity V = jn*QD in
the end-effector frame.

See also

q = R.jtraj(T1, t2, k, options) is a joint space trajectory (KxN) where
the joint coordinates reflect motion from end-effector pose T1 to t2 in k
steps with default zero boundary conditions for velocity and
acceleration. The trajectory q has one row per time step, and one column
per joint, where N is the number of robot joints.

Options

'ikine', F

A handle to an inverse kinematic method, for example
F = @p560.ikunc. Default is ikine6s() for a 6-axis spherical
wrist, else ikine().

Additional options are passed as trailing arguments to the inverse
kinematic function.

See also

m = R.maniplty(q, options) is the manipulability index (scalar) for the
robot at the joint configuration q (1xN) where N is the number of robot
joints. It indicates dexterity, that is, how isotropic the robot's
motion is with respect to the 6 degrees of Cartesian motion. The measure
is high when the manipulator is capable of equal motion in all directions
and low when the manipulator is close to a singularity.

If q is a matrix (MxN) then m (Mx1) is a vector of manipulability
indices for each joint configuration specified by a row of q.

[m,ci] = R.maniplty(q, options) as above, but for the case of the Asada
measure returns the Cartesian inertia matrix ci.

Two measures can be computed:

Yoshikawa's manipulability measure is based on the shape of the velocity
ellipsoid and depends only on kinematic parameters.

Asada's manipulability measure is based on the shape of the acceleration
ellipsoid which in turn is a function of the Cartesian inertia matrix and
the dynamic parameters. The scalar measure computed here is the ratio of
the smallest/largest ellipsoid axis. Ideally the ellipsoid would be
spherical, giving a ratio of 1, but in practice will be less than 1.

Options

'T'

manipulability for transational motion only (default)

'R'

manipulability for rotational motion only

'all'

manipulability for all motions

'dof', D

D is a vector (1x6) with non-zero elements if the
corresponding DOF is to be included for manipulability

'yoshikawa'

use Yoshikawa algorithm (default)

'asada'

use Asada algorithm

Notes

The 'all' option includes rotational and translational dexterity, but
this involves adding different units. It can be more useful to look at the
translational and rotational manipulability separately.

Examples in the RVC book can be replicated by using the 'all' option

References

Analysis and control of robot manipulators with redundancy,
T. Yoshikawa,
Robotics Research: The First International Symposium (M. Brady and R. Paul, eds.),
pp. 735-747, The MIT press, 1984.

Notes

See also

rp = R.perturb(p) is a new robot object in which the dynamic parameters (link
mass and inertia) have been perturbed. The perturbation is multiplicative so
that values are multiplied by random numbers in the interval (1-p) to (1+p).
The name string of the perturbed robot is prefixed by 'p/'.

Useful for investigating the robustness of various model-based control
schemes. For example to vary parameters in the range +/- 10 percent is:

R.plot(q, options) displays a graphical animation of a robot based on
the kinematic model. A stick figure polyline joins the origins of
the link coordinate frames. The robot is displayed at the joint angle q (1xN), or
if a matrix (MxN) it is animated as the robot moves along the M-point trajectory.

Options

'workspace', W

Size of robot 3D workspace, W = [xmn, xmx ymn ymx zmn zmx]

'floorlevel', L

Z-coordinate of floor (default -1)

'delay', D

Delay betwen frames for animation (s)

'fps', fps

Number of frames per second for display, inverse of 'delay' option

'[no]loop'

Loop over the trajectory forever

'[no]raise'

Autoraise the figure

'movie', M

Save frames as files in the folder M

'trail', L

Draw a line recording the tip path, with line style L

'scale', S

Annotation scale factor

'zoom', Z

Reduce size of auto-computed workspace by Z, makes
robot look bigger

'ortho'

Orthographic view

'perspective'

Perspective view (default)

'view', V

Specify view V='x', 'y', 'top' or [az el] for side elevations,
plan view, or general view by azimuth and elevation
angle.

'top'

View from the top.

'[no]shading'

Enable Gouraud shading (default true)

'lightpos', L

Position of the light source (default [0 0 20])

'[no]name'

Display the robot's name

'[no]wrist'

Enable display of wrist coordinate frame

'xyz'

Wrist axis label is XYZ

'noa'

Wrist axis label is NOA

'[no]arrow'

Display wrist frame with 3D arrows

'[no]tiles'

Enable tiled floor (default true)

'tilesize', S

Side length of square tiles on the floor (default 0.2)

'tile1color', C

Color of even tiles [r g b] (default [0.5 1 0.5] light green)

'tile2color', C

Color of odd tiles [r g b] (default [1 1 1] white)

'[no]shadow'

Enable display of shadow (default true)

'shadowcolor', C

Colorspec of shadow, [r g b]

'shadowwidth', W

Width of shadow line (default 6)

'[no]jaxes'

Enable display of joint axes (default false)

'[no]jvec'

Enable display of joint axis vectors (default false)

'[no]joints'

Enable display of joints

'jointcolor', C

Colorspec for joint cylinders (default [0.7 0 0])

'jointdiam', D

Diameter of joint cylinder in scale units (default 5)

'linkcolor', C

Colorspec of links (default 'b')

'[no]base'

Enable display of base 'pedestal'

'basecolor', C

Color of base (default 'k')

'basewidth', W

Width of base (default 3)

The options come from 3 sources and are processed in order:

Cell array of options returned by the function PLOTBOTOPT (if it exists)

Cell array of options given by the 'plotopt' option when creating the
SerialLink object.

List of arguments in the command line.

Many boolean options can be enabled or disabled with the 'no' prefix. The
various option sources can toggle an option, the last value is taken.

Graphical annotations and options

The robot is displayed as a basic stick figure robot with annotations
such as:

shadow on the floor

XYZ wrist axes and labels

joint cylinders and axes

which are controlled by options.

The size of the annotations is determined using a simple heuristic from
the workspace dimensions. This dimension can be changed by setting the
multiplicative scale factor using the 'mag' option.

Figure behaviour

If no figure exists one will be created and the robot drawn in it.

If no robot of this name is currently displayed then a robot will
be drawn in the current figure. If hold is enabled (hold on) then the
robot will be added to the current figure.

If the robot already exists then that graphical model will be found
and moved.

Multiple views of the same robot

If one or more plots of this robot already exist then these will all
be moved according to the argument q. All robots in all windows with
the same name will be moved.

Create a robot in figure 1

figure(1)
p560.plot(qz);

Create a robot in figure 2

figure(2)
p560.plot(qz);

Now move both robots

p560.plot(qn)

Multiple robots in the same figure

Multiple robots can be displayed in the same plot, by using "hold on"
before calls to robot.plot().

Create a robot in figure 1

figure(1)
p560.plot(qz);

Make a clone of the robot named bob

bob = SerialLink(p560, 'name', 'bob');

Draw bob in this figure

hold on
bob.plot(qn)

To animate both robots so they move together:

qtg = jtraj(qr, qz, 100);
for q=qtg'

p560.plot(q');
bob.plot(q');

end

Making an animation movie

The 'movie' options saves frames as files NNNN.png into the specified folder

The specified folder will be created

To convert frames to a movie use a command like:

ffmpeg -r 10 -i %04d.png out.avi

Notes

The options are processed when the figure is first drawn, to make different options come
into effect it is neccessary to clear the figure.

The link segments do not neccessarily represent the links of the robot, they are a pipe
network that joins the origins of successive link coordinate frames.

By default a quite detailed plot is generated, but turning off labels,
axes, shadows etc. will speed things up.

Each graphical robot object is tagged by the robot's name and has UserData
that holds graphical handles and the handle of the robot object.

The graphical state holds the last joint configuration

The size of the plot volume is determined by a heuristic for an all-revolute
robot. If a prismatic joint is present the 'workspace' option is
required. The 'zoom' option can reduce the size of this workspace.

See also

R.plot3d(q, options) displays and animates a solid model of the robot.
The robot is displayed at the joint angle q (1xN), or
if a matrix (MxN) it is animated as the robot moves along the M-point trajectory.

Options

'color', C

A cell array of color names, one per link. These are
mapped to RGB using colorname(). If not given, colors
come from the axis ColorOrder property.

'alpha', A

Set alpha for all links, 0 is transparant, 1 is opaque
(default 1)

'path', P

Overide path to folder containing STL model files

'workspace', W

Size of robot 3D workspace, W = [xmn, xmx ymn ymx zmn zmx]

'floorlevel', L

Z-coordinate of floor (default -1)

'delay', D

Delay betwen frames for animation (s)

'fps', fps

Number of frames per second for display, inverse of 'delay' option

'[no]loop'

Loop over the trajectory forever

'[no]raise'

Autoraise the figure

'movie', M

Save frames as files in the folder M

'scale', S

Annotation scale factor

'ortho'

Orthographic view (default)

'perspective'

Perspective view

'view', V

Specify view V='x', 'y', 'top' or [az el] for side elevations,
plan view, or general view by azimuth and elevation
angle.

'[no]wrist'

Enable display of wrist coordinate frame

'xyz'

Wrist axis label is XYZ

'noa'

Wrist axis label is NOA

'[no]arrow'

Display wrist frame with 3D arrows

'[no]tiles'

Enable tiled floor (default true)

'tilesize', S

Side length of square tiles on the floor (default 0.2)

'tile1color', C

Color of even tiles [r g b] (default [0.5 1 0.5] light green)

'tile2color', C

Color of odd tiles [r g b] (default [1 1 1] white)

'[no]jaxes'

Enable display of joint axes (default true)

'[no]joints'

Enable display of joints

'[no]base'

Enable display of base shape

Notes

Solid models of the robot links are required as STL ascii format files,
with extensions .stl

Suitable STL files can be found in the package ARTE: A ROBOTICS TOOLBOX
FOR EDUCATION by Arturo Gil, https://arvc.umh.es/arte

The root of the solid models is an installation of ARTE with an empty
file called arte.m at the top level

Each STL model is called 'linkN'.stl where N is the link number 0 to N

The specific folder to use comes from the SerialLink.model3d property

The path of the folder containing the STL files can be specified using
the 'path' option

The height of the floor is set in decreasing priority order by:

'workspace' option, the fifth element of the passed vector

'floorlevel' option

the lowest z-coordinate in the link1.stl object

Authors

Peter Corke, based on existing code for plot()

Bryan Moutrie, demo code on the Google Group for connecting ARTE and RTB

See also

qs = R.qmincon(q) exploits null space motion and returns a set of joint
angles qs (1xN) that result in the same end-effector pose but are away
from the joint coordinate limits. N is the number of robot joints.

[q,err] = R.qmincon(q) as above but also returns err which is the
scalar final value of the objective function.

[q,err,exitflag] = R.qmincon(q) as above but also returns the
status exitflag from fmincon.

Trajectory operation

In all cases if q is MxN it is taken as a pose sequence and R.qmincon()
returns the adjusted joint coordinates (MxN) corresponding to each of the
poses in the sequence.

err and exitflag are also Mx1 and indicate the results of optimisation
for the corresponding trajectory step.

Notes

Requires fmincon from the Optimization Toolbox.

Robot must be redundant.

Author

Bryan Moutrie

See also

tau = R.rne(q, qd, qdd) is the joint torque required for the robot R to
achieve the specified joint position q (1xN), velocity qd (1xN) and
acceleration qdd (1xN), where N is the number of robot joints.

See also

R.teach(q, options) allows the user to "drive" a graphical robot by means
of a graphical slider panel. If no graphical robot exists one is created
in a new window. Otherwise all current instances of the graphical robot
are driven. The robots are set to the initial joint angles q.

R.teach(options) as above but with options and the initial joint angles
are taken from the pose of an existing graphical robot, or if that doesn't
exist then zero.

Options

'eul'

Display tool orientation in Euler angles (default)

'rpy'

Display tool orientation in roll/pitch/yaw angles

'approach'

Display tool orientation as approach vector (z-axis)

'[no]deg'

Display angles in degrees (default true)

'callback', CB

Set a callback function, called with robot object and
joint angle vector: CB(R, Q)

Example

To display the velocity ellipsoid for a Puma 560

p560.teach('callback', @(r,q) r.vellipse(q));

GUI

The specified callback function is invoked every time the joint configuration changes.
the joint coordinate vector.

The Quit (red X) button destroys the teach window.

Notes

If the robot is displayed in several windows, only one has the
teach panel added.

The slider limits are derived from the joint limit properties. If not
set then for

a revolute joint they are assumed to be [-pi, +pi]

a prismatic joint they are assumed unknown and an error occurs.

See also

s = R.TRCHAIN(options) is a sequence of elementary transforms that describe the
kinematics of the serial link robot arm. The string s comprises a number
of tokens of the form X(ARG) where X is one of Tx, Ty, Tz, Rx, Ry, or Rz.
ARG is a joint variable, or a constant angle or length dimension.